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Bounding the Family-Wise Error Rate in Local Causal Discovery Using Rademacher Averages

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Machine Learning and Knowledge Discovery in Databases (ECML PKDD 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13717))

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Abstract

Many algorithms have been proposed to learn local graphical structures around target variables of interest from observational data. The Markov boundary (MB) provides a complete picture of the local causal structure around a variable and is a theoretically optimal solution for the feature selection problem. Available algorithms for MB discovery have focused on various challenges such as scalability and data-efficiency. However, current approaches do not provide guarantees in terms of false discoveries in the MB.

In this paper we introduce a novel algorithm for the MB discovery problem with rigorous guarantees on the Family-Wise Error Rate (FWER), that is, the probability of reporting any false positive. Our algorithm uses Rademacher averages, a key concept from statistical learning theory, to properly account for the multiple-hypothesis testing problem arising in MB discovery. Our evaluation on simulated data shows that our algorithm properly controls for the FWER, while widely used algorithms do not provide guarantees on false discoveries even when correcting for multiple-hypothesis testing. Our experiments also show that our algorithm identifies meaningful relations in real-world data.

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Notes

  1. 1.

    N counts, in fact, the total number of possible conditional independencies between any couple of variables by considering the symmetry property of independence tests, that is testing the (conditional) independence of X from Y is equivalent to testing the one of Y from X.

  2. 2.

    Code and appendix available at https://github.com/VandinLab/RAveL.

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Acknowledgements

This work is supported, in part, by the Italian Ministry of Education, University and Research (MIUR), under PRIN Project n. 20174LF3T8 “AHeAD” (efficient Algorithms for HArnessing networked Data) and the initiative “Departments of Excellence” (Law 232/2016), and by University of Padova under project “SID 2020: RATED-X”.

Author information

Authors and Affiliations

  1. Department of Information Engineering, University of Padova, Padua, Italy

    Dario Simionato & Fabio Vandin

Authors
  1. Dario Simionato
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  2. Fabio Vandin
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Corresponding author

Correspondence to Fabio Vandin .

Editor information

Editors and Affiliations

  1. Grenoble Alpes University, Saint Martin d’Hères, France

    Massih-Reza Amini

  2. INSA Rouen Normandy, Saint Etienne du Rouvray, France

    Stéphane Canu

  3. Ruhr-Universität Bochum, Bochum, Germany

    Asja Fischer

  4. KU Leuven, Leuven, Belgium

    Tias Guns

  5. Central European University, Vienna, Austria

    Petra Kralj Novak

  6. Aristotle University of Thessaloniki, Thessaloniki, Greece

    Grigorios Tsoumakas

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Simionato, D., Vandin, F. (2023). Bounding the Family-Wise Error Rate in Local Causal Discovery Using Rademacher Averages. In: Amini, MR., Canu, S., Fischer, A., Guns, T., Kralj Novak, P., Tsoumakas, G. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2022. Lecture Notes in Computer Science(), vol 13717. Springer, Cham. https://doi.org/10.1007/978-3-031-26419-1_16

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  • DOI: https://doi.org/10.1007/978-3-031-26419-1_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-26418-4

  • Online ISBN: 978-3-031-26419-1

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